Stability conditions on derived categories
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DissertationDate of Exam
07.05.2008Date of Publication
2008Advisor
Huybrechts, DanielCo-Referee
Rapoport, MichaelMetadata
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Abstract
My thesis is divided into two parts. In the first part I consider stability conditions on the derived category of complex manifolds without any nontrivial subvarieties. In particular, I construct and classify stability conditions in the case of generic K3 surfaces, generic tori and general deformations of Hilbert schemes of K3 surfaces.
The second part is devoted to the analysis of quotient categories. The main theorem of the second part states that the quotient category of the derived category of a surface modulo complexes supported in codimension two has homological dimension one. I apply this to describe the quotient category obtained by modding out Mumford-stable objects of degree zero.
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Classification (DDC)
510 MathematikOnline-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-14856
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-14856,
author = {{Sven Meinhardt}},
title = {Stability conditions on derived categories},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2008,
note = {
My thesis is divided into two parts. In the first part I consider stability conditions on the derived category of complex manifolds without any nontrivial subvarieties. In particular, I construct and classify stability conditions in the case of generic K3 surfaces, generic tori and general deformations of Hilbert schemes of K3 surfaces.
The second part is devoted to the analysis of quotient categories. The main theorem of the second part states that the quotient category of the derived category of a surface modulo complexes supported in codimension two has homological dimension one. I apply this to describe the quotient category obtained by modding out Mumford-stable objects of degree zero.
url = {https://hdl.handle.net/20.500.11811/3651}
}
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